Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE?
1. If $f(z)$ is differentiable at $z_{0}$, then $g(z)$ and $h(z)$ are also differentiable at $z_{0}$.
2. If $g(z)$ and $h(z)$ are differentiable at $z_{0}$, then $f(z)$ is also differentiable at $z_{0}$.
3. If $f(z)$ is continuous at $z_{0}$, then it is differentiable at $z_{0}$.
4. If $f(z)$ is differentiable at $z_{0}$, then so are its real and imaginary parts